CN109379124A - Weighted subspace adaptive antenna directional diagram secondary lobe shape accuracy control method - Google Patents

Weighted subspace adaptive antenna directional diagram secondary lobe shape accuracy control method Download PDF

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CN109379124A
CN109379124A CN201810992478.5A CN201810992478A CN109379124A CN 109379124 A CN109379124 A CN 109379124A CN 201810992478 A CN201810992478 A CN 201810992478A CN 109379124 A CN109379124 A CN 109379124A
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secondary lobe
weighting
adaptive
subspace
directional diagram
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CN109379124B (en
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马晓峰
周淼
盛卫星
韩玉兵
张仁李
崔杰
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Nanjing University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/2813—Means providing a modification of the radiation pattern for cancelling noise, clutter or interfering signals, e.g. side lobe suppression, side lobe blanking, null-steering arrays
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0857—Joint weighting using maximum ratio combining techniques, e.g. signal-to- interference ratio [SIR], received signal strenght indication [RSS]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Variable-Direction Aerials And Aerial Arrays (AREA)

Abstract

The invention discloses a kind of weighted subspace adaptive antenna directional diagram secondary lobe shape accuracy control methods, comprising the following steps: is distributed according to beam position and desired sidelobe level and determines secondary lobe weighting function；Secondary lobe area guiding performance vector is weighted using secondary lobe weighting function, secondary lobe covariance matrix is calculated using the secondary lobe area guiding performance vector after weighting, takes its main feature vector building secondary lobe subspace matrices；Adaptive weighting is projected to secondary lobe subspace matrices, passes through its modulus value of inequality constraints；By the inequality constraints and MVDR optimization problem simultaneous, improved MVDR cost function is formed；Adaptive weighting is solved using interior point method.The present invention is accurately directed toward desired signal in guarantee main lobe, while Adaptive Suppression secondary lobe area's stepwise derivation, adaptive direction figure peak sidelobe can be accurately controlled to inhibit burst to interfere, and have complicated secondary lobe area level distribution control ability, to be suitable for special airspace interference and clutter recognition scene.

Description

Weighted subspace adaptive antenna directional diagram secondary lobe shape accuracy control method
Technical field
The invention belongs to the anti-interference fields in array antenna airspace, and in particular to a kind of weighted subspace adaptive antenna direction Figure secondary lobe shape accuracy control method.
Background technique
Self-adaptive numerical integration algorithm technology is particularly advantageous in that it can be directed toward the phase guaranteeing antenna radiation pattern main lobe It hopes and adaptively generates null in interference radiating way while signal.Foremost self-adaptive numerical integration algorithm device is minimum variance It is undistorted response (Minimum Variance Distortionless Response, MVDR) Beam-former and by popularization And linear constraint minimal variance (Linear Constraint Minimum Variance, the LCMV) Beam-former come, it Be all that the output power of Beam-former is minimized under conditions of meeting given linear restriction to adaptively inhibit dry It disturbs.
MVDR Beam-former can indicate are as follows:
W=argminwHRxw s.t.wHa(θ0)=1.
But dry out fastly to some times and disturb, especially the interference of burst form, adaptive beam former are usual Have little time or the weight coefficient that can not timely update generates adaptive nulling, causes the output performance of Beam-former to decline. Low sidelobe control technology also has certain inhibiting effect to such interference in the case where not updating weight coefficient.Another party Face, high-precision target angle estimation and tracking generally use and poor Monopulse estimation technology.And Monopulse estimation requires angle measurement Wave beam has stable main lobe shape and direction, if main lobe deformation or peakdeviation, not only influence angle measurement accuracy, but also can lead Cause output Signal to Interference plus Noise Ratio decline.Traditional MVDR and LCMV Beam-former does not often have steady major lobe of directional diagram control energy Power receives data model error when existing, such as low snap, main lobe signal, in the case of guiding performance vector error or array error, Major lobe of directional diagram characteristic can severe exacerbation.Therefore, research adaptive antenna Pattern control is particularly important while more in order to cope with The interference of sample and clutter, complicated secondary lobe shape control are also most important.
Diagonal load is a kind of Sidelobe control method of classics, improves association by artificially injecting noise in covariance matrix The robustness of variance matrix, so that directional diagram is avoided significantly to shake, but diagonal loading amount is generally difficult to determine；Penalty function side Method is reached by allowing adaptive direction figure or adaptive weighting to approach pre-optimized good static directional diagram or static weight To the purpose of control sidelobe level, however such method is generally unable to accurately control the peak sidelobe of adaptive direction figure, With less complicated secondary lobe shape control ability.Document 1 (R.Wu, Z.Bao, Y.L.Ma, " Control of peak sidelobe level in adaptive arrays,”IEEE Transactions on Antennas&Propagation, Vol.44, no.10,1996, pp.1341-1347.) the penalty function model of its proposition is solved by diagonal loading method, and derive Accurate numerical relation between diagonal loading amount and expectation peak sidelobe out, may be implemented peak side-lobe using this relationship Level accurately controls, but its accuracy depends on suitable static weight；Document 2 (J.Liu, A.B.Gershman, Z.Q.Luo,et al.,“Adaptive beamforming with sidelobe control:a second-order cone programming approach,”IEEE Signal Processing letters,vol.10,no.11,2003, Pp.331-334. sidelobe level) is directly controlled using the constraint of multiple quadratic inequalities, this method guarantees the peak side-lobe of optimization Level is located at desired value hereinafter, still computationally intensive, and the major lobe of directional diagram be directed toward it is unstable.
Summary of the invention
The purpose of the present invention is to provide a kind of, and the adaptive antenna directional diagram secondary lobe shape based on weighted subspace is accurate Control method, by accurately controlling directional diagram peak sidelobe with the interference of suppressed sidelobes area burst, while by certainly Null suppressed sidelobes area stepwise derivation is adapted to, and guarantees that main lobe stablizes accurate direction desired signal.
Realize the technical solution of the object of the invention are as follows: a kind of weighted subspace adaptive antenna directional diagram secondary lobe shape is accurate Control method, comprising the following steps:
Step 1, it is distributed according to beam position and desired sidelobe level and determines secondary lobe weighting function；
Step 2, secondary lobe area guiding performance vector is weighted using secondary lobe weighting function, is led using the secondary lobe area after weighting Tropism vector calculates secondary lobe covariance matrix, takes its main feature vector building secondary lobe subspace matrices；
Step 3, adaptive weighting is projected to secondary lobe subspace matrices, passes through its modulus value of inequality constraints；By this differ Formula constraint and MVDR optimization problem simultaneous, form improved MVDR cost function；
Step 4, adaptive weighting is solved using interior point method.
Compared with prior art, the present invention its remarkable advantage are as follows: (1) present invention can accurately control adaptive direction figure peak It is worth sidelobe level, realizes complicated secondary lobe shape control, has steady main lobe shape and be directed toward control ability；(2) present invention is logical It crosses single Subspace Constrained to control entire secondary lobe, increases the numerical stability of weight solution；It is empty in construction secondary lobe Between when, introduce the weighting function determining by the distribution of expectation sidelobe level, achieve the purpose that fitting expectation sidelobe level distribution；(3) The present invention can substantially reduce constraint dimension by Subspace Constrained, reduce computational complexity；Algorithm can be converted into SOCP problem, Interior point method Efficient Solution can be passed through；(4) this method computation complexity is low, can be widely applied to radar, communication, sonar, radio day Text, the adaptive array antenna in the systems such as Speech processing.
Detailed description of the invention
Fig. 1 is algorithm implementation flow chart of the invention.
Fig. 2 (a), Fig. 2 (b), Fig. 2 (c) be respectively in embodiment 50 array element uniform straight line arrays in different expectation sidelobe levels Adaptive direction figure under distribution.
Fig. 3 is fast with sampling there are Signal to Interference plus Noise Ratio is exported under a main lobe signal and two secondary lobe disturbed conditions in embodiment The change curve of umber of beats.
Specific embodiment
In conjunction with Fig. 1, a kind of adaptive antenna directional diagram secondary lobe shape accuracy control method based on weighted subspace, including Following steps:
Step 1, it is distributed according to beam position and desired sidelobe level and determines secondary lobe weighting function.
Step 2, secondary lobe area guiding performance vector is weighted using secondary lobe weighting function, is led using the secondary lobe area after weighting Tropism vector calculates secondary lobe covariance matrix, takes its main feature vector building secondary lobe subspace matrices；
Step 3, adaptive weighting is projected to secondary lobe subspace matrices, passes through its modulus value of inequality constraints；By this differ Formula constraint and MVDR optimization problem simultaneous, form improved MVDR cost function；
Step 4, adaptive weighting is solved using interior point method.
Further, step 1 specifically:
Step 1-1, building secondary lobe weight subfunction h1(θ)；
It is assumed that directional diagram expectation beam position is θ0, secondary lobe area range is Θ, and desired sidelobe level distribution function is DSL (θ), θ ∈ Θ, unit dB.So, peak sidelobe can be expressed as DPSLA=10(max(DSL(θ))/20), θ ∈ Θ. It takesThe weighting subfunction is uniformly distributed for controlling adaptive direction figure sidelobe level；
Step 1-2, building secondary lobe weight subfunction h2(θ)；
Take h2(θ)=10(-DSL(θ)/20), θ ∈ Θ, which, which realizes, it is expected the control of secondary lobe shape；
Step 1-3 constructs final secondary lobe weighting function h (θ)=h1(θ)×h2(θ), θ ∈ Θ.
Further, step 2 specifically:
Step 2-1, building weighting secondary lobe covariance matrix RΘ；
J angle, θ is uniformly chosen in secondary lobe area Θj, j=1,2 ..., J, according to formulaCalculate weighting secondary lobe covariance matrix RΘ, a (θj) it is array guiding performance vector, J > > N, N are battle array First number guarantees RΘFor non-singular matrix.Index p is arranged according to desired sidelobe level distribution function DSL (θ), if only needing to control Adaptive direction figure peak sidelobe, to secondary lobe shape no requirement (NR), then p=0, i.e., without weighting；Otherwise p=1 guarantees to add Weight function h (θ) is effective.
Step 2-2 constructs secondary lobe area constraint matrix VΘ；
To RΘEigenvalues Decomposition is carried out, characteristic value is arranged in descending order, λnFor RΘN-th of characteristic value, vnReturn to be corresponding One changes feature vector；M feature vector constitutes secondary lobe subspace V before takingΘ=[v1,v2,...,vM], with VΘAbout as secondary lobe area Beam matrix.
Further, step 3 specifically:
Determine optimal beam forming device Optimized model；
The cost function of optimization problem is
In above formula, RxFor array received signal covariance estimated matrix, can be expressed asWherein K To sample number of snapshots, x (k) is array received signal vector.wHa(θ0)=1 is desired signal unit gain constraint,For the inequality constraints of secondary lobe subspace, DPSLA=10(max(DSL(θ))/20)For desired peak sidelobe width Degree.
According to foregoing description, summarizing implementation method of the invention, steps are as follows:
1, pre-treatment step:
1) according to beam position θ0Secondary lobe weighting function h is successively calculated with desired sidelobe level distribution function DSL (θ)1 (θ), h2(θ) and h (θ).
2) secondary lobe covariance matrix R is calculated using the secondary lobe area guiding performance vector a (θ) after h (θ) weightingΘ, to RΘIt carries out Eigenvalues Decomposition takes RΘPreceding M feature vector constitute secondary lobe subspace matrices VΘ；
2, self-adaptive processing step:
3) adaptive weighting vector is projected to secondary lobe subspace matrices, passes through its modulus value of inequality constraints；By this differ Formula constraint and MVDR optimization problem simultaneous, form improved MVDR cost function.
4) adaptive weighting is solved using interior point method.
It elaborates combined with specific embodiments below with attached drawing to the present invention.
Embodiment
The invention proposes one kind accurately to control adaptive direction figure peak sidelobe by weighted subspace, and has The adaptive antenna radiation pattern control method of complicated secondary lobe area level distribution control ability, method flow diagram are as shown in Figure 1.
The present embodiment uses the 50 equidistant uniform straight line arrays of array element half-wavelength, and element antenna is isotropic omnidirectional antennas Line does not consider mutual coupling existing between elements.Signal comes from 0 ° of direction, and unit signal-to-noise ratio is 10dB；Two secondary lobe interference are respectively from+50 ° With -50 ° of directions, unit is dry to make an uproar than being 45dB；Noise is unit additive white Gaussian noise, and interference and signal space and time are not It is related.The present embodiment realizes A, tri- kinds of B, C different expectation sidelobe level distributed controlls, secondary lobe area Θ=[- 90 °, -3.5 °] ∪ [3.5°,90°].A: the peak sidelobe of adaptive direction figure is no more than -30dB；B: adaptive direction figure peak sidelobe No more than -30dB, and sidelobe level constant amplitude is distributed；C: adaptive direction figure sidelobe level is in [- 40 °, -10 °] region from -30dB It is reduced to -45dB along oblique line (slope is -1/2), is -40dB in [20 °, 40 °] region, remaining region is -30dB.
It should be based on the adaptive antenna directional diagram secondary lobe shape essence of weighted subspace under the uniform straight line array of this 50 array element The realization of true control method includes the following steps:
Step 1: according to beam position θ0=0 and desired sidelobe level be distributed determine secondary lobe weighting function.
To A: only peak sidelobe amplitude DPSLA=10-30/20；
To B:DSL (θ)=- 30, DPSLA=10-30/20,h2(θ)=10-DSL(θ)/20, h (θ)=h1 (θ)×h2(θ)；
To C:DPSLA=10-30/20, h2(θ)=10-DSL(θ)/20, h (θ)=h1(θ)×h2(θ)。
Step 2: uniformly choosing J angle, θ in Θ=[- 90 °, -3.5 °] ∪ [3.5 °, 90 °] in secondary lobe areaj, then root According to formulaCalculate weighting secondary lobe covariance matrix RΘ, a (θj) it is array guiding performance vector, J > > N=50 guarantees RΘFor non-singular matrix.To A, due to only controlling adaptive direction figure peak sidelobe, it is not necessarily to weighting function, P=0；To B and C, p=1.To RΘEigenvalues Decomposition is carried out, characteristic value is arranged in descending order, λnFor RΘN-th of characteristic value, vn For corresponding normalization characteristic vector；M main feature vectors constitute secondary lobe subspace V before takingΘ=[v1,v2,...,vM], M=N- 1=49, with VΘAs secondary lobe area constraint matrix.
Step 3: determining optimal beam forming device Optimized model；
The cost function of optimization problem is
Step 4: optimal weights being solved using interior point method, the SeDuMi solver in the tool box MATLAB CVX point can be passed through It Qiu Xie not adaptive weighting vector w.
For this example, A is set forth in Fig. 2 (a), Fig. 2 (b), Fig. 2 (c), under tri- kinds of expectation sidelobe level distributions of B, C Adaptive direction figure, sampling number of snapshots be 100, carry out 50 Monte Carlo independent experiments.It can be seen that under three kinds require, Adaptive direction figure main lobe shape and beam position maintain to stablize, and secondary lobe very well satisfies wanting for desired sidelobe level distribution It asks, peak sidelobe is below -30dB.The distribution of adaptive direction figure sidelobe level constant amplitude and Fig. 2 in especially Fig. 2 (b) (c) adaptive direction figure secondary lobe area has accurately been fitted the dual area constant amplitude and the distribution of oblique line Low sidelobe level of C in, illustrates the present invention Secondary lobe shape control ability is prominent.Also, adaptive nulling effectively generates in the case of three kinds, and the null of two interference positions is deep Degree is below -60dB.Fig. 3 gives output Signal to Interference plus Noise Ratio with the situation of change of sampling number of snapshots, carries out 200 Monte Carlos Independent experiment.It can be seen that output Signal to Interference plus Noise Ratio tends to optimal value, and algorithm ensure that desired signal as number of snapshots increase Good reception, and interference and noise are effectively inhibited simultaneously, due to the average side lobe electricity of adaptive direction figure in the case of three kinds Flat difference causes its main lobe width and signal gain to slightly have difference, and then exports Signal to Interference plus Noise Ratio slight difference.

Claims (4)

1. a kind of adaptive antenna directional diagram secondary lobe shape accuracy control method based on weighted subspace, which is characterized in that packet Include following steps:
Step 1, it is distributed according to beam position and desired sidelobe level and determines secondary lobe weighting function；
Step 2, secondary lobe area guiding performance vector is weighted using secondary lobe weighting function, using the secondary lobe area guiding performance after weighting Vector calculates secondary lobe covariance matrix, takes its main feature vector building secondary lobe subspace matrices；
Step 3, adaptive weighting is projected to secondary lobe subspace matrices, passes through its modulus value of inequality constraints；About by the inequality Beam and MVDR optimization problem simultaneous, form improved MVDR cost function；
Step 4, adaptive weighting is solved using interior point method.
2. the adaptive antenna directional diagram secondary lobe shape accurate controlling party according to claim 1 based on weighted subspace Method, which is characterized in that step 1 specifically:
Step 1-1, building secondary lobe weight subfunction h1(θ)；
Assuming that directional diagram expectation beam position is θ0, secondary lobe area range is Θ, and desired sidelobe level distribution function is DSL (θ), θ ∈ Θ, unit dB；So, peak sidelobe is represented by DPSLA=10(max(DSL(θ))/20), θ ∈ Θ；It takesThe weighting subfunction is uniformly distributed for controlling adaptive direction figure sidelobe level；
Step 1-2, building secondary lobe weight subfunction h2(θ)；
Take h2(θ)=10(-DSL(θ)/20), θ ∈ Θ, which, which realizes, it is expected the control of secondary lobe shape；
Step 1-3 constructs final secondary lobe weighting function h (θ)=h1(θ)×h2(θ), θ ∈ Θ.
3. the adaptive antenna directional diagram secondary lobe shape accurate controlling party according to claim 1 based on weighted subspace Method, which is characterized in that step 2 specifically:
Step 2-1, building weighting secondary lobe covariance matrix RΘ；
J angle, θ is uniformly chosen in secondary lobe area Θj, j=1,2 ..., J, according to formula Calculate weighting secondary lobe covariance matrix RΘ, a (θj) it is array guiding performance vector, J > > N, N are array number, guarantee RΘFor full rank square Battle array；Index p is arranged according to desired sidelobe level distribution function DSL (θ), if only needing to control adaptive direction figure peak side-lobe Level, to secondary lobe shape no requirement (NR), then p=0, i.e., without weighting；Otherwise p=1 guarantees that weighting function h (θ) is effective；
Step 2-2 constructs secondary lobe area constraint matrix VΘ；
To RΘEigenvalues Decomposition is carried out, characteristic value is arranged in descending order, λnFor RΘN-th of characteristic value, vnFor corresponding normalization Feature vector；M feature vector constitutes secondary lobe subspace V before takingΘ=[v1,v2,...,vM], with VΘSquare is constrained as secondary lobe area Battle array.
4. the adaptive antenna directional diagram secondary lobe shape accurate controlling party according to claim 1 based on weighted subspace Method, which is characterized in that step 3 specifically:
Determine Beam-former Optimized model；
The cost function of optimization problem is
In above formula, RxFor array received signal covariance estimated matrix, it is expressed asWherein K is sampling snap Number, x (k) are array received signal vector；wHa(θ0)=1 is desired signal unit gain constraint,For secondary lobe Space inequality constraints, DPSLA=10(max(DSL(θ))/20)For desired peak sidelobe amplitude.
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